OK, and you stated that you confirmed that your password is correct by logging into your email online with the same email and password, correct?
That error message that you're receiving is directly related to the login credentials for that specific email account (Email/Password) -- more specifically it's referring to SMTP, which is the outgoing server (IMAP or POP would be the incoming server).
Go ahead and go into your Mail application > Click Mail in the top left menu bar > Choose Preferences > Choose Accounts > Choose the email account you're experiencing issues with (if you have more than one listed).
Once you're within the email account preferences make sure you're under the "Account Information" tab. Delete the password that appears about halfway down and re-enter it, making certain it's the same password you used successfully to login to your email web portal. Then in the "Outgoing Mail Server (SMTP)" section, choose "Edit SMTP server list". Choose the server name in the list that you use as your outgoing email server. Under the "Advanced" tab, be certain that your email and password are listed. Once again, delete what's in the password field and re-enter the password you know to be correct. Than click "OK", click the red circle to close out of the "Accounts" window. Choose to Save/Apply changes when prompted.
Then go back to Window (in the menu bar) > Connection Doctor and have a look and see if you get all green indicator dots now.
Good luck!